Abstract

A line-by-line radiative-transfer model to quantify the Ring effect
as caused by rotational Raman scattering has been developed for the
310–550-nm spectral interval. The solar zenith angle and the
resolution are key input parameters, as is the sky spectrum
(excluding inelastic atmospheric scattering), which was modeled
with modtran3.5. The filling in is modeled for
ground-based viewing geometry and includes surface reflection and
single inelastic scattering. It is shown that O2
contributes half of the filling in of N2. A strong
inverse relationship with wavelength is noted in the filling in. A
comparison with observations shows moderate agreement. The largest
filling in occurs in the Ca ii K and H lines.

Effect of ignoring terrestrial absorption on FI
values. The sky spectrum and the solar spectrum (both with a
resolution of 22 cm-1 (a FWHM of a triangular slit
function) (at a SZA of 60°) are compared. The difference in
FI occurring in the near-UV region is primarily due to Huggins band gas
absorption lines (O3).

Sum of cross sections shifting radiance due to RRS
(σin versus σout),
O2, 410–434 nm. Each point on the thick line
represents the sum of the rotational Raman cross sections for the lines
shifting light out of that wavelength. The points on the thin line
indicate the intensity-weighted cross sections for lines shifting light
into a particular wavelength. Note the inverse wavelength
dependence for both. The difference between corresponding points on
the thick and the thin lines is the cross section inputted into the
Beer’s law formalism to obtain the frequency-redistributed intensity
at a particular wavelength.

RRS/Rayleigh phase function ratio versus scattering
angle. The weaker dependence of Raman scattering on the cosine of
the scattering angle is responsible for the maximum (at 90°) in
the ratio of phase functions (RRS/Rayleigh) versus scattering
angle.

FI spectrum in the 310–410-nm spectral interval at a
resolution of 22 cm-1 (FWHM of the triangular slit
function); SZA, 30°. Note the large FI for the Ca
ii K and H lines at approximately 393 and 397 nm,
respectively.

Spectral radiance of skylight (Wcm-2
cm-1 sr-1) with and without RRS (thin and
thick lines, respectively) for the Ni i line near 313 nm
at an SZA of 30°. There is FI in the line core and the opposite
effect in the wings of the line (at ∼313.9 nm) and in the nearby
continuum.